Liu-type shrinkage estimations in linear models

In this study, we present the preliminary test, Stein-type and positive part Liu estimators in linear models when parameter vector β is partitioned into two parts, namely, main effects β1 nuisance β2 such that β=(β1,β2). We consider case a priori known or suspected set of explanatory variables do not contribute to predict response so sub-model may be enough for purpose. Thus, interest estimate close zero. Therefore, investigate performance suggested asymptotically via Monte Carlo simulation study. Moreover, real data example evaluate relative efficiency estimators, where demonstrate superiority proposed estimators.